Create Realistic Lips Without Sculpting Them From Scratch?
So I actually figured out how to do it. For anyone who might be interested in my process, here goes. I realized that the picture I took of my own lips was a poor quality picture because the lighting was uneven and that caused a lot of bumpiness when I anchored the image on my character in sculpt mode. When I used a picture with even lighting, it automatically looked way better and needed a lot less clean up. To prep this photo, I used Gimp to create a high-quality image for the sculpting brush I created in Blender 2.82. 

As far as settings, I used the Clay sculpt brush with the full strength of 1.00, Mapping is set to "Area Plane," Stroke method is set to "Anchored" in the remesh section, Voxel Size is set to 0.1800, and I did have to do some massive clean up for the face, but they were small details that needed to be removed. Lastly, I did need to use the "Crease" brush with "Stabilize Stroke" on with default settings. I also used the "Grab," "Snake Hook," "Nudge," and "Smooth" brushes to get the shape correct and the texture even. Since I have multiple copies of my character saved, I used the original copy of my characters' face as a reference to correct all the facial proportions after the lips texture was finished (Images used as sculpt brushes will slightly change the proportions of the character). 

I sculpted to remove details that were incorrect leaving only details that looked pretty decent to me. This is by no means hyper-realistic but that's not my goal. It looks good enough for me and I'm happy with it. I still need to properly color the lips and create a gradient for all the colors, but this picture shows how it turned out. For anyone who only wants to use sculpting to remove unnecessary details without actually having to create the detailed creases of the lips from scratch, this is what worked for me. Hopefully, this helps someone.